Question

How do you simplify `2/3 + 1/5 - 1/2`?

Answer 1

`11/30`

Explanation:

`color(blue)("Considering the common denominator")`

5 will be a factor of any number (apart from 0) that end in 5 or 10
Unfortunately a number ending with 5 can not be divided exactly by 2. So the common denominator has to be a one of the 'tens'

Note that `3xx10 = 30 =>` the common factor is 30
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Method of changing to equivalent fractions")`

Multiply a number by 1 and you do not change its value. You can however change the way it looks.
Example: `3xx1 -= 3xx5/5 -=15/5`

The inherent value is still three but it looks different.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Write as: `(2/3xx10/10)+(1/5xx6/6)-(1/2xx15/15)`

`( (2xx10)/(3xx10) )+((1xx6)/(5xx6))-((1xx15)/(2xx15))`

`20/30+6/30-15/30`

`color(brown)("You can now directly add/subtract the top numbers")`

`(20+6-15)/30 =11/30`